(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that [tex]\sum(-1)^n\frac{n}{p_n}[/tex] converges, where [tex]p_n[/tex] is the nth prime.

2. Relevant equations

The sequence [tex]\frac{n}{p_n}[/tex] is definately not monotone if there exists infinitely many twin primes, since [tex]2n-p_n<0[/tex] for sufficiently large n, so alternating series test is out. Are there any other ways of showing this converges?

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# Homework Help: Prove that the series SUM (-1)^n n/p_n converges where p_n are primes

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